For this project, we used the dot product with genetics data. The angle between the two vectors demonstrates how closely related the two populations are. This is found using the dot product, as the dot product of two vectors is equivalent to the product of the lengths of the vectors and the cosine of the angle between them. So, to find the angle, we isolated theta and used the equation below to solve for the angles between all five of our populations. Using the allele frequencies from the first four genes listed, we created our vectors and conducted the calculations to find genetic closeness. We then created a DNA double helix in Mathematica. For this, we took the formula for a circle in parametric equations and added a z element, and stacked two of these spirals on top of each other for the signature DNA double helix.
We included some extra research about what genes are and how the dot product interacts. The dot product is very commonly used to determine genetic closeness and is helpful for predicting drug effects by testing them on closely related animals. The smaller the angle, the more closely related the two populations are. Due to the nature of randomly choosing four genes to do our calculations with, our data is not going to be as accurate as using more or all of the genes we found on the website. For example, our most closely related populations were white caucasian and Native American racial groups. This could have happened because the genes were not representative of the populations or because the racial groups were self-reported, and someone who is culturally one ethnicity isn’t necessarily genetically that ethnicity.
